CPT created with CustomPress won't let editor-level users (no role editing) create new content

We’re using CustomPress to create CPTs AND Advanced Custom Fields to manage our fields. We have not edited the default roles and our CPTs all have “capability type” set to “post” yet our users with role set to “editor” cannot create new content.

Attempts to post content to a CPT throw up the “You are not allowed to edit this post” message. Any ideas?

Running WP 3.4.1, CustomPress and Advanced Custom Fields 3.3.9.